To determine the relationship between rational numbers and whole numbers, we need to understand what each term means:
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Rational Numbers: A rational number is any number that can be expressed as the quotient or fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). This includes integers, fractions, and finite or repeating decimals.
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Whole Numbers: Whole numbers are all non-negative integers, which include 0, 1, 2, 3, and so on.
Now, let's analyze the numbers -3 and 7 in relation to these definitions:
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Number 7:
- 7 is a whole number (it is non-negative and an integer).
- 7 can also be expressed as a rational number: \( \frac{7}{1} \), where both 7 and 1 are integers and the denominator is not zero. Therefore, 7 is a rational number.
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Number -3:
- -3 is not a whole number because whole numbers do not include negative integers.
- However, -3 is a rational number, as it can be expressed as \( \frac{-3}{1} \).
From these points, we can conclude that:
- Not all rational numbers are whole numbers (as -3 is a rational number but not a whole number).
- All whole numbers are rational numbers (as 7 is both a whole number and a rational number).
In summary, while all whole numbers (like 7) are indeed rational numbers, not all rational numbers (like -3) are whole numbers.